Download File

Geometry A
6.1 Properties of Parallelograms
Name _________________________
Hour _______ Date ______________
Assignment
Find each indicated measure in parallelogram ABCD.
1. AB = __________
2. BC = __________
Find each indicated measure in parallelogram ABCD.
3. mB = ___________
4. mC = ___________
5. mD = ___________
VWXY is a parallelogram. Find each indicated measure. Show all calculations.
6. VX = __________
7. XZ = __________
8. ZW = __________
9. WY = __________
Suppose that AB has endpoints A(-3, 6) and B(1, -4).
10. Find the length of AB .
11. Find the midpoint of AB .
12. Find the slope of AB
Geometry A
6.2 Proving a Quadrilateral is a Parallelogram
Name _________________________
Hour _______ Date ______________
Assignment
Determine whether a figure with the given vertices is a parallelogram. Justify your answer.
1.
Q(-6, -6), R(2, 2), S(-1, 6), T(-5, 2); Show all calculations.
Use the slope formula.
Parallelogram? _________ Justification ____________________________________________________
2.
W(-6, -5), X(-1, -4), Y(0, -1), Z(-5, -2); Show all calculations.
Use the distance formula.
Parallelogram? _________ Justification ____________________________________________________
3.
H(5, 6), J(9, 0), K(8, -5), L(3, 2); Show all calculations.
Use the midpoint formula.
Parallelogram? _________ Justification ____________________________________________________
Geometry A
6.3 Properties of Rectangles
Name _________________________
Hour _______ Date ______________
Assignment
ABCD is a rectangle.
1.
If AC = 2x + 13 and DB = 4x – 1, find x. Show your calculations.
2.
If AC = x + 3 and DB = 3x – 19, find AC. Show your calculations.
3.
If mDAC  2x  4 and mBAC  3x  1 , find x. Show your calculations.
4.
If mBDC  7 x  1 and mADB  9x  7 , find mCBD . Show your calculations.
5.
Is there enough information to state that the figure below is a parallelogram? ________
Justification ________________________________________________________
6.
R is between J and K. Find n if JR = 2n – 12, RK = 3n + 10, and JK = 33 cm.
7.
If m7  5x  5 and m8  4x  14 , find the value of x.
Geometry A
6.4 Proving a Quadrilateral is a Rectangle
Name _________________________
Hour _______ Date ______________
Assignment
1.
Determine whether W(-4, 5), X(6, 0), Y(3, -6), and Z(-7, -1) are vertices of a rectangle. Show all work.
(Hint: use the midpoint formula and distance formula).
WXYZ is / is not a rectangle.
Justification: _________________________________________________________________.
2.
3.
WXYZ is a parallelogram. Find each indicated value.
a = _______
m  YWX = ___________
m  YWZ = _________
m  XYZ = ___________
Find the perimeter of RST .
5y + 18
7y – 6
4.
Given: A and B are vertical angles.
Conjecture: A ≅ B
Which of the following would be a counterexample to the conjecture?
A.
B.
C.
D.
mA  45 and mB  45
mA  100 and mB  80
mA  90 and mB  90
None of the above, because the conjecture is true.
Geometry B
6.5 Properties of Rhombi and Squares
Name _________________________
Hour ______ Date _______________
Assignment
In rhombus ABCD, BE = 18, and AE = 24.
1. AB = _______
5. CE = _______
2. BC = _______
6. AC = _______
3. AD = _______
7. DB = _______
4. DE = _______
8. m AED = ______
In rhombus STVR, m  STN = 25o.
9. m  VTN = _______
13. m  VRT = _______
10. m  TVS = _______
14. m  RST = _______
11. m  RVS = _______
15. m  STV = _______
12. m  SRT = _______
16. m  RNV = _______
In rhombus RSTV, RS = 5y + 2, ST = 3y + 6, NV = 6, and mNTV = 30o.
17. Find the value of y. Show all calculations.
18. Find TV. Show all calculations.
Identify the triangle congruence postulate that could be used to prove that each pair of triangles are
congruent based on the given information. If it is not possible to prove that the triangles are congruent,
choose “not possible.”
19.
20.
21.
22.
Geometry A
6.6 Proving that a Quadrilateral is a Rhombus or a Square
Name _________________________
Hour _______ Date ______________
Assignment
Given each set of vertices, determine whether QRST is a parallelogram, rhombus, rectangle, or square.
List all that apply. Justify your reasoning. Show all calculations.
1.
Q(-4, 5), R(4, 1), S(1, -5), T(-7, -1)
QRST is a (circle all that apply)
Parallelogram
2.
Square
5
6
and
3
10
B.
5
20
and
3
12
C. 
5
10
and
3
6
D.
5
9
and 
3
15
Which one of the following pairs of slopes are slopes corresponding to perpendicular lines?
A.
4.
Rhombus
Which one of the following pairs of slopes are slopes corresponding to parallel lines?
A.
3.
Rectangle
5
6
and
3
10
B.
5
20
and
3
12
C. 
5
10
and
3
6
D.
5
9
and 
3
15
Which angle pair are  11 and  16 in the figure at the right?
A. Vertical Angles (VA)
B. Corresponding Angles (CA)
C. Alternate Interior Angles (AIA)
D. Alternate Exterior Angles (AEA)
E. Consecutive Interior Angles (CIA)
Geometry A
6.7 Trapezoids
Name _________________________
Hour ______ Date _______________
Assignment
1. For trapezoid EFGH, J and K are the midpoints
of the legs. Find JK. Show all calculations.
E
17
F
J
K
H
2. For trapezoid FGHI, K and M are the midpoints
of the legs. Find FI, F and I . Show all
calculations.
G
31
3. In trapezoid MNQR, B and C are midpoints of
the legs. Let AD be the median of MNCB.
4. In trapezoid HIJK, L and M are midpoints of the
legs. Let NP be the median of LMJK.
a. Draw and label AD
on the figure.
a. Draw and label NP
on the figure.
M
22
C
B
b. Find AD.
Show all calculations.
R
N
48
b. Find NP.
Show all calculations.
Q
H
39
M
L
K
I
55
J
5. Verify that A(-3, -2), B(4, -2), C(-1, 5), and D(2, 5), are vertices of a trapezoid. Justify your answer.
ABCD is a trapezoid.
Justification: ______________________________________________________
6.
CDEF is a parallelogram. m  D = 47o. Find the indicated values.
m  C = _______
m  E = _______
m  F = _______
7. ABCD is a rectangle. If mDAC = 7x + 1 and mBAC = 9x – 7, find mDCA. Show all calculations.
In problems #8 and 9, r || s. Solve for x, then find the measures of the indicated angles.
8. m4  x  35, m6  4x 10
9. m5  6 x  12, m4  7 x  9
x = _____, m4  _____ , m2  _____
x = _____, m4  _____ , m6  _____
State the property, definition, theorem, or postulate that justifies each statement.
10.
CD = CD. _______________________________
11.
If AB  BC and BC  CE , then AB  CE . _____________________________________
12.
If N is between M and P, then MN + NP = MP. ___________________________________
13.
If MN  PQ , then PQ  MN . _____________________________
14.
If m7  m8  85o and m8  41o , then m7  41o  85o . _____________________________
15.
If R is the midpoint of QT , then QR  RT . _______________________________
Geometry A
6.8 Kites & Quadrilaterals
Name _________________________
Hour ______ Date _______________
Assignment
8 cm
1. EFGH is a kite with ends F and H. If EG = 30 cm, find the indicated lengths and angle measures.
F
EB = ______
BG = ________
62ᵒ
E
G
20 cm
B
EF = ______
FG = _______
EH = ______
GH = _______
mGBH = _______
mBEF  ________
H
2. Given ABCD is a kite with ends A and C, solve for x and find all missing side lengths.
A
B
D
27
2x + 13
C
3. Verify that A(1, -3), B(4, -2), C(3, 1), and D(-2, 1), are vertices of a kite. Justify your answer.
ABCD is a kite.
Justification: ______________________________________________________
For # 4-11, fill in the blanks.
4.
The diagonals of a parallelogram ____________________ one another.
5.
Opposite angles of a parallelogram are ______________________.
6.
Opposite sides of parallelograms are ______________________ and ________________________.
7.
Consecutive angles of parallelograms are ________________________.
8.
The diagonals of a rectangle are ________________________.
9.
All angles of a rectangle are ________________________.
10.
The diagonals of a rhombus are ______________________ and ______________________________.
11.
All sides of a rhombus are ___________________________.
12.
Complete the following proof:
Given: C is the midpoint of AD
C is the midpoint of BE
Prove: ABC  DEC
Statements
Reasons
1. C is the midpoint of AD
1.
2.
2. Midpoint Theorem
3. C is the midpoint of BE
3.
4.
4. Midpoint Theorem
5.
5. Vertical Angles Theorem
6. ABC  DEC
6.
Geometry A
6.9 Constructions of Quadrilaterals
Name _________________________
Hour ______ Date _______________
Assignment
1.
Construct a parallelogram.
2.
Construct a square.
3.
Construct a line that is parallel to line n, passing through point A.
n
A
4.
Construct the bisector of M .
M
5.
6.
Construct a triangle with side lengths given below.
Determine whether the quadrilateral with the given vertices is a parallelogram, rectangle, rhombus, or
square. Circle all that apply. Show all calculations.
B(0, 3), E(6, -2), F(1, -8), G(-5, -3)
BEFG is a (circle all that apply)
Parallelogram
Rectangle
Rhombus
Square